1. Suppose that a random sample of 41 state college students is asked to measure the length of their right foot in centimeters. A 95% confidence interval for the mean foot length for students at this university turns out to be (21.709, 25.091). Which of the following is true?
A. The sample mean was 23.4 cm.
B. The margin of error is 3.382.
C. If the confidence level is changed to 90% we will get a wider interval.
2. Scores this year for students taking the SAT Mathematics (SAT-M) test for the first time are believed to be Normally distributed with mean µ1. For students taking the test for the second time, this year's scores are also believed to be Normally distributed, but with a possibly different mean µ2. The standard deviations for first- and second-time test takers appear to stay relatively constant from year to year and can be taken to be known, with value σ1 = 100 for first-time takers and value 2 = 90 for second-time takers. We wish to estimate the difference µ2 - µ1. A random sample was obtained of the SAT-M scores of 100 students who took the test for the first time this year and the mean of these 100 scores was 1 = 504.5. A random sample was also obtained of the SAT-M scores of 36 students who took the test for the second time this year and the mean of these 36 scores was 2 = 539.1. A 95% confidence interval for µ2 - µ1 is
A. 34.6 ± 29.66.
B. 34.6 ± 35.33.
C. 34.6 ± 35.97.